If $_nP_r = 30240$ and $\binom{n}{r} = 252$,then $(n, r) = \dots$

$A$ question paper contains $4$ questions,each having $4$ alternative answers. The number of ways that a candidate can answer one or more questions is

The last two digits of $2015! + 3^{2015}$ are:

On her vacations,Veena visits four cities ($A, B, C$,and $D$) in a random order. What is the probability that she visits $A$ either first or second?

How many words can be formed using $3$ consonants and $2$ vowels from $5$ consonants and $4$ vowels?

If all the letters of the word $ACADEMICIAN$ are permuted in all possible ways,then the number of permutations in which no two $A$'s are together and all the consonants are together is: